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On semi-fredholm properties of a boundary value problem inR + n
Authors:Jouko Tervo
Affiliation:1. Department of Mathematics, University of Jyv?skyl?, Seminaarinkatu 15, SF-40100, Jyv?skyl?, Finland
Abstract:The paper considers a boundary value problem with the help of the smallest closed extensionL :H kH k 0×B h 1×...×B h N of a linear operatorL :C (0) (R + n ) →L(R + n L(R n−1)×...×L(R n−1). Here the spacesH k (the spaces ℬ h ) are appropriate subspaces ofD′(R + n ) (ofD′(R n−1), resp.),L(R + n ) andC (0) (R + n )) denotes the linear space of smooth functionsR n C, which are restrictions onR + n of a function from the Schwartz classL (fromC 0 , resp.),L(R n−1) is the Schwartz class of functionsR n−1C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L ) and for the uniqueness of solutionsL U=F are expressed. In addition, ana priori estimate for the corresponding boundary value problem is established.
Keywords:
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